\usepackage{cite}
\usepackage[pdftex]{graphicx}  
\usepackage[cmex10]{amsmath}
\usepackage{bibspacing}
\setlength{\bibspacing}{\baselineskip}
%\usepackage{algorithmic}
%\usepackage{array}
%\usepackage{mdwmath}
%\usepackage{mdwtab}
%\usepackage{eqparbox}
%\usepackage[tight,footnotesize]{subfigure}
\usepackage{subfigure}
%\usepackage[caption=false]{caption}
%\usepackage[font=footnotesize]{subfig}
%\usepackage[caption=false,font=footnotesize]{subfig}
%\usepackage{fixltx2e}
%\usepackage{stfloats}
%\usepackage{url}

% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***

\usepackage{calc}

\usepackage{amssymb,amsmath,mathrsfs}     %%% MATHEMATICAL SYMBOLS
\usepackage[vlined, ruled, linesnumbered]{algorithm2e}
\usepackage[]{color}

\newtheorem{lemma}{Lemma}
\newtheorem{Observation}{Observation}
\newtheorem{Example}{Example}
\newtheorem{Property}{Property}
\newcommand{\argmax}{\operatornamewithlimits{argmax}}

\newcommand{\todo}[1]{{\color{red}todo: #1\\}}


\newcommand{\Treqprof}[1]{\mathbb{T}_{#1}}
\newcommand{\SamplingRegionSize}[1]{L^{\operatorname{reg-size}}_{#1}}
\newcommand{\Regions}[1]{\mathbb{G}_{#1}}
\newcommand{\Requests}[1]{\mathbb{R}_{#1}}
\newcommand{\NbReqPerRegion}[2]{\eta_{#1, #2}}
\newcommand{\NbReqPerTask}[1]{\eta_{(#1)}}
\newcommand{\request}[2]{\operatorname{req}_{#1, #2}}
%\newcommand{\reqrel}[2]{\operatorname{rel}_{#1, #2}}
%\newcommand{\reqserv}[2]{\operatorname{serv}_{#1, #2}}
\newcommand{\reqrel}[2]{r_{#1, #2}}
\newcommand{\reqserv}[2]{s_{#1, #2}}
\newcommand{\BusAvailability}[1]{\mathbb{B}_{#1}}
\newcommand{\Tmin}[2]{T^{\min}_{#1}(#2)}
\newcommand{\Tmax}[2]{T^{\max}_{#1}(#2)}
\newcommand{\Assignment}[2]{\alpha_{#1}(#2)}
\newcommand{\SetOfConstraints}[1]{\mathbb{C}_{#1}}
\newcommand{\LBslot}[2]{\operatorname{LBslot}_{#1, #2}}
\newcommand{\UBslot}[2]{\operatorname{UBslot}_{#1, #2}}
\newcommand{\LBTime}[2]{\operatorname{LBTime}_{#1, #2}}
\newcommand{\UBTime}[2]{\operatorname{UBTime}_{#1, #2}}
\newcommand{\TaskLBslot}[1]{\operatorname{LBslot}_{#1}}
\newcommand{\TaskUBslot}[1]{\operatorname{UBslot}_{#1}}
\newcommand{\TaskLBTime}[1]{\operatorname{LBTime}_{#1}}
\newcommand{\TaskUBTime}[1]{\operatorname{UBTime}_{#1}}
%\newcommand{\tsum}{\operatorname{tsum}}
\newcommand{\CumulDelay}[1]{D(#1)}
\newcommand{\AllAssignments}[3]{\operatorname{FBS}_{#1}^{#2}(#3)}
\newcommand{\AllAssignmentSlot}[3]{\operatorname{FBS}_{#1}^{#2}(#3)}
\newcommand{\GroupAssign}[4]{A^{#2, #4}_{#1}(#3)}
\newcommand{\Delay}[4]{D^{#2, #4}_{#1}(#3)}
\newcommand{\SDelay}[3]{D^{#2}_{#1}(#3)}
\newcommand{\Sreqrel}[4]{r^{#2, #4, #3}_{#1}}
\newcommand{\Sreqserv}[4]{s^{#2, #4, #3}_{#1}}
\newcommand{\Assign}[5]{\alpha^{#2, #4, #3}_{#1}(#5)}
\newcommand{\Constant}[1]{C_{#1}^{\operatorname{st}}}

\newcommand{\AssignmentOne}[2]{\alpha_{#1}(#2)}
\newcommand{\AssignmentTwo}[2]{\alpha_{#1}'(#2)}
\newcommand{\DelayOne}[2]{D_{#1}(#2)}
\newcommand{\DelayTwo}[2]{D_{#1}'(#2)}
\newcommand{\reqrelOne}[2]{r_{#1,#2}}
\newcommand{\reqrelTwo}[2]{r_{#1,#2}'}
\newcommand{\reqservOne}[2]{s_{#1,#2}}
\newcommand{\reqservTwo}[2]{s_{#1,#2}'}


\newcommand{\frameSize}{\ensuremath{\textit{f}}}
\newcommand{\slots}{\ensuremath{\phi}}
\newcommand{\PCRE}{{\operatorname{PCRE}}}
\newcommand{\TR}{{\operatorname{TR}}}
\newcommand{\MaxRegDelay}{{\operatorname{MaxRegDelay}}}
%Previous definitions
%\newcommand{\SumRequests}{{\operatorname{SumRequests}}}
%\newcommand{\TS}{{\operatorname{TS}}}
%\newcommand{\PCRE}{{\operatorname{PCRE}}}
%\newcommand{\equals}{\stackrel{\operatorname{def}}{=}}
%\newcommand{\TR}{\widehat{\operatorname{TR}}}
%\newcommand{\BR}[1]{\operatorname{BR_{#1}^{iso}}}
%\newcommand{\trel}{\operatorname{trel}}
%\newcommand{\tsrv}{\operatorname{tsrv}}
%\newcommand{\td}{\operatorname{td}}
%\newcommand{\tdsum}{\operatorname{tdsum}}
%\newcommand{\tdmax}{\operatorname{tdmax}}
%\newcommand{\numslot}{\operatorname{numslot}}
%\newcommand{\Nslots}{\operatorname{Nslots}}
%\newcommand{\Nreq}{\operatorname{Nreq}}
%\newcommand{\pslot}{\operatorname{pslot}}
%\newcommand{\fslot}[1]{\operatorname{slot}({#1})}
%\newcommand{\timefslot}[1]{t(#1)}
%\newcommand{\released}{\operatorname{rel}}
%\newcommand{\served}{\operatorname{svd}}
%\newcommand{\delay}[1]{d_{#1}}
%\newcommand{\Delay}[1]{D(#1)}
%\newcommand{\maxdelay}{\hat{d}}
%\newcommand{\WCCD}{\operatorname{WCCD}}
%\newcommand{\UBtime}{\operatorname{UBtime}}
%\newcommand{\LBtime}{\operatorname{LBtime}}
%\newcommand{\rqid}{\operatorname{rid}}
%\newcommand{\slotid}{\operatorname{slotid}}
